Phase variation in free-electron laser amplifiers

The evolution of the phase of the output radiation of free-electron laser amplifiers is investigated by means of a three-dimensional simulation code. The configuration employed consists of the propagation of a relativistic electron beam through a loss-free cylindrical waveguide in the presence of a helically symmetric wiggler and a uniform axial guide magnetic field. The analysis is fully three dimensional, and a set of model equations is discussed which describes the coupling between an ensemble of electrons and the radiation field of either the TE or TM modes. The model equations are solved numerically, and the output phase is studied with respect to variations in either frequency or electron beam energy. The output phase is found to depend sensitively on the wave frequency within the unstable bandwidth. In addition, the phase stability of the output radiation is discussed as a function of beam energy. Finally, the evolution of the phase for tapered wiggler free-electron lasers is studied.